If the expression below has a negative value, which inequality represents all possible values of n in the expression?

The area of the composite figure in which the length of squares is 1.5 cm is 49.1 [tex]cm^{2}[/tex]

Given that the grid has squares with side lengths of 1.5 cm.

We are required to find the area of the composite figure.

The area of the composite figure is approximate to the area of the rectangle plus the are of the semicircle at the top of the rectngle plus the semicircle at the right side of the rectangle.

Finding the area of the rectangle.

A=(3*1.5)(4*1.5)=27 [tex]cm^{2}[/tex]

Finding the area of the semicircle at the top of the rectangle.

A=1/2 π[tex](2*1.5)^{2}[/tex]=4.5 π [tex]cm^{2}[/tex]

Finding the area of the semicircle at the right of the rectangle.

A=1/2 π[tex](1.5*1.5)^{2}[/tex]

=2.53π [tex]cm^{2}[/tex]

Total area =27+4.5π+2.53π

=27+7.03π

Use π=3.14

=27+7.03*3.14

=49.1 [tex]cm^{2}[/tex]

Hence the area of the composite figure in which the length of squares is 1.5 cm is 49.1 [tex]cm^{2}[/tex].

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Answer:

The painter was more productive in week a.

Step-by-step explanation:

Find the unit rate.  How many houses could be painted in 1 day?

6/2 means that she could paint 3 houses per day

5/4 means that she could paint 1.25 houses per day.

The painter was more productive in the last week.

In this problem, we need to find in which week did the painter paint the most.

To find the solution to this problem, first, we need to divide 6 by 2 (last week)

which equals 3.

Next, divide 5 by 4 (this week)

which equals 1.25

Now, compare the two quotients and identify the larger number (3 and 1.25).

Basically, we can see that the number 3 is larger.

This means that the painter could paint 3 houses per day in the last week, and 1.25 houses per day in this week.

Therefore, we can say that the painter was more productive in the last week.

I hope this helps :)

Volume of prism = [tex]\frac{1}{2x^{3} } + x^{2}[/tex]

Given that:

The oblique prism below has an isosceles right triangle base and the length of the base is x

=> the area of the base: [tex]\frac{1}{2}[/tex] × x × x = [tex]\frac{1}{2}[/tex]

The vertical height of the prism is (x + 2)

=> The volume of the oblique prism is:

                    V = the base area * the vertical height

<=> V = [tex]\frac{1}{2}[/tex] [tex]x^{2}[/tex] (x + 2)

<=> V =  [tex]\frac{1}{2x^{3} } + x^{2}[/tex]

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Answer:

division

Step-by-step explanation:

ratio compares 2 numbers by dividing them

example

2 out of 3 dentists like gum

2 ÷ 3 = .67 = 67%

so you can say

67% of dentists like gum

A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one. For example, if the number of marks scored in a test is 7 out of 10, then the ratio of marks obtained to the total number of marks is written as 7:10.

Answer:

assuming it's a perfect world and that the fish lives in a 1 cubic meter fish tank 1*1.4422 will increase the volume my a factor of 3

The expression [tex]\sqrt[4]{\frac{24x^6y}{128x^4y^5} }[/tex] is equivalent to the expression [tex]\frac{\sqrt[4]{3x^2}}{2y}[/tex]

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Given the expression:

[tex]\sqrt[4]{\frac{24x^6y}{128x^4y^5} }\\ \\Simplifying:\\\\=\frac{\sqrt[4]{3x^2}}{2y}[/tex]

The expression [tex]\sqrt[4]{\frac{24x^6y}{128x^4y^5} }[/tex] is equivalent to the expression [tex]\frac{\sqrt[4]{3x^2}}{2y}[/tex]

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Answer:

The answer is D

Step-by-step explanation:

Answer:

-2/3

Step-by-step explanation:

A rational number is a number that can be expressed as a fraction so when you add 2 fractions it’s a rational number

Answer:

3

Step-by-step explanation:

-2 * 3= -6

-1 * 3= -3

0 *3= 0

1 *3 = 3

2* 3 = 6

3 * 3 =9

Answer:

? = 3

Step-by-step explanation:

To find the value of ?, substitute one of the ordered pairs from the table [except (0, 0)] into the given formula and solve for ?.

Given formula:

[tex]\sf y=\boxed{?} \:x[/tex]

Substitute x = 1 and y = 3 into the formula:

[tex]\sf 3=\boxed{?} \:1[/tex]

To isolate ? divide both sides by 1:

[tex]\implies \sf \dfrac{3}{1}=\dfrac{\boxed{?} \:1}{1}[/tex]

[tex]\implies \sf 3=\boxed{?}[/tex]

Therefore, ? = 3:

[tex]\implies \sf y=3x[/tex]

Check by inputting another value of x from the table into the found formula and comparing the calculated y-value:

[tex]\sf x=-2 \implies y=3(-2)=-6 \quad \boxed{\sf correct}[/tex]

[tex]\sf x=3 \implies y=3(3)=9 \quad \boxed{\sf correct}[/tex]

7. ∠I and ∠M are corresponding angles.

8. ∠J and ∠P are alternate exterior angles.

9. ∠K and ∠M are alternate interior angles.

10. ∠L and ∠M are consecutive interior angles..

11. ∠I and ∠O are alternate exterior angles.

12. 7. ∠K and ∠O are corresponding angles.

Angles that are formed outside the parallel lines that are intersected by a transversal and lie alternate to each other on along the transversal are alternate exterior angles.

Angles that are formed inside of the parallel lines that are intersected by a transversal and lie alternate to each other on along the transversal are alternate interior angles.

Angles that are formed inside of the parallel lines that are intersected by a transversal and lie on the same side of the the transversal are consecutive interior angles.

Angles that are formed in relative corner position on each of the parallel lines that are intersected by a transversal and lie along the transversal in the same side are called corresponding angles.

Thus, from the image given, we have the following special angles:

7. ∠I and ∠M are corresponding angles.

8. ∠J and ∠P are alternate exterior angles.

9. ∠K and ∠M are alternate interior angles.

10. ∠L and ∠M are consecutive interior angles..

11. ∠I and ∠O are alternate exterior angles.

12. 7. ∠K and ∠O are corresponding angles.

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Answer:

A. because 5 < 6. 1-(-4)=5. and 4-(-2) =6

Answer:

4 degrees ( to nearest degree).

Step-by-step explanation:

The trig ratio you want is the tangent.

tan x = 10,000 / 160,000    where x is the angle of depression.

tan x = 0.0625

x = 3.576 degrees.

Answer:

Step-by-step explanation:

We know a total of 6000 is being turned into 510, in two accounts which equal to 15%, to find how much is in each account we can create the following equation:

[tex]5x+10x=510[/tex]

Solve for x

[tex]15x=510\\x=34[/tex]

Now multiply x by the corresponding percentages to find how much was invested into each percentage.

[tex]34*5=170[/tex]

[tex]34*10=340[/tex]

Therefore we now know that 170 dollars was invested into the 5% division, and 340 dollars was invested into the 10% division.

We can of course check our answer by adding 170+340 which equals our original investment of 510.

$1800 is invested at 5% and the remainder, $4200, is invested at 10%.

percentage, a relative value indicating hundredth parts of any quantity.

Let us consider the amount invested at 5% x.

The amount invested at 10% is then the remainder, which is:

$6000 - x

Now we can set up an equation for the total interest earned:

0.05x + 0.10($6000 - x) = $510

Simplifying and solving for x:

0.05x + $600 - 0.10x = $510

-0.05x + $600 = $510

-0.05x = -$90

Divide both sides by 0.05

x = $1800

Hence, $1800 is invested at 5% and the remainder, $4200, is invested at 10%.

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Answer:

  140 cm

Step-by-step explanation:

The distance of the foot of the ladder from the building can be found using the Pythagorean theorem (or your knowledge of Pythagorean triples). Once the two distances are found, their difference can be found.

The 650 cm ladder reaches 520 cm up the side of the building. The ratio of these side lengths is 650/520 = 5/4, suggesting these are the sides of a 3-4-5 right triangle. The distance from the building is ...

  (3/5)×650 cm = 390 cm.

Alternatively, the distance (a) from the building can be found using the Pythagorean relation ...

  a² +b² = c²

  a² +520² = 650²

  a = √(422500 -270400) = √152100 = 390 . . . cm

The 650 cm ladder reaches 520 +80 = 600 cm up the side of the building. The ratio of these side lengths is 650/600 = 13/12, suggesting these are the sides of a 5-12-13 right triangle. The distance from the building is ...

  (5/13)×650 cm = 250 cm

Again, the Pythagorean theorem can be used to obtain the same result:

  a = √(422500 -360000) = √62500 = 250 . . . cm

The difference between the two distances is ...

  390 cm -250 cm = 140 cm

The foot of the ladder will be 140 cm closer to the building.

Answer:

175 cal

Step-by-step explanation:

if 12oz = 300 cal

then, 7 oz = ?

cross multiplication

12×?= 7×300

? = 2100/12

? = 175 cal

NB: you can replace the question mark with any variable.

Based on the graph of the budget function with the x-intercept and the y-intercept, the two ordered pairs that would fall on this line are (2, 0) (0, 5).

The x-intercept is the point on the graph where the budget function would cross the x-intercept.

At this point, the value of y would be 0 because the x-axis intersects the y-axis at y = 0.

An x-intercept of 2 would therefore have the point, (2,0).

The y-intercept would be the point where the y axis is crossed. At this point, x will be zero because the y-axis intercepts the x-axis at the value, x = 0.

A y-intercept of 5 would therefore yield a point of (0, 5).

In conclusion, option A is correct.

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The explicit form of the arithmetic function as described is; f(p) = 2(p-1) + 12. and the seventh term is; 24.

Since it follows from the task content, that the first term is 12 and the common difference is 2.

It therefore follows from convention that the explicit function is; f(p) = 2(p-1) + 12 and by substituting n= 7 into, the equation, we have; f(7) = 24.

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James is (B) 20 meters far from the finish line 9 seconds after the race has started.

To find the distance:

Therefore, James is (B) 20 meters far from the finish line 9 seconds after the race has started.

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The complete question is given below:

James covers a distance of 8 meters in the first second of a 100-meter race. Then, he sprints at a speed of 9 meters per second. How far is James from the finish line 9 seconds after the race has started?

a. 11

b. 20

c. 28

d. 80

Answer:

a^2+b^2=c^2

Step-by-step explanation:

leg1=a

leg2=b

hypotenuse=c

a^2+b^2=c^2

Answer:

u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D

Step-by-step explanation:      

The null hypothesis to test the claim that the proportion of people who owns cats is larger than 60% of the significance level is [tex]H_{0}[/tex]:μ<0.06.

Given that the significance level is 0.10.

We are required to form the null hypothesis to test the claim that the proportion of people who owns cats is larger than 60% the significance level.

Hypothesis is a statement which is tested for its validity. Null hypothesis is the statement which is accepted or not by z test,t test,f test ,chi-square test or any other test.

We have to take opposite of the statement to form a null hypothesis. Since we have to check whether the proportion of people who owns cats is larger than 60% of the significance level, we have to assume that it is smaller than 60% of the significance level.

60% of the significance level=0.60*0.10=0.06.

Null hypothesis is [tex]H_{0}[/tex]:μ<0.06

Hence the null hypothesis to test the claim that the proportion of people who owns cats is larger than 60% of the significance level is [tex]H_{0}[/tex]:μ<0.06.

Question is incomplete.The question should include the following:

Find the null hypothesis for the testing.

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For the given diagram, it has been proved that angle A is congruent to angle B.

Given Information:

Angle A and Angle B are such that,

Ray AC ║ Ray BE

Ray AD ║ Ray BF

Proof:

Since a straight line is the shortest line connecting two points in a plane,

Extend ray AD and ray BE, such that both intersect at point G.

Now, since, angle A and angle 1 both make corresponding angles,

∠A = ∠1 .......... (1)

Ray ADG is parallel to the ray BF.

Thus, again, angle B and angle 1 make corresponding angles,

∠B = ∠1 ............ (2)

From (1) and (2), as per transitive relationship of angles,

∠A ≅ ∠B

Hence proved.

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Answer:

c=3.

Step-by-step explanation:

∵2*2*2=8,

∴2^3=8.

∵2^c=8,

∴c=3.

When to use the law of cosine is explained below.

Using the labelled triangle, we have: sin D/d = sin E/e = sin F/f.

Using the sine law, the measure of angle M is: 74.9°.

The cosine law is given as, c = a² + b² - 2ab(cos C). It is used to solve a triangle with missing angle or side.

When we are given two sides and an angle between the two sides, and we need to find the third side.

When we are given the all three sides of a triangle and we need to find the angles of the triangle.

Using the labelled triangle DEF in the diagram below, the law of sines is:

sin D/d = sin E/e = sin F/f.

m∠N = 56°

n = 8.5 cm

m = 9.9 cm

Plug in the values into sin N/n = sin M/m:

sin 56/8.5 = sin M/9.9

sin M = (sin 56 × 9.9)/8.5

sin M = 0.9656

M = sin^(-1)(0.9656)

M = 74.9°

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When graphing, the intersections of the graphs represent the solutions of the system.

When graphing a system of equations, you just need to graph both equations in the same coordinate axis.

The solutions of the system are all the points where the graphs of the two equations intersect.

This means that if there is only one intersection, there is one solution.

But we can have more than one intersection, like in the case where at least one of the equations is a polynomial of degree 2 or more.

And there is also the case that the graphs never intersect, like in parallel lines, in these cases we have no solutions.

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Answer:

[tex]\textsf{a)} \quad v=12t^2-6t-18[/tex]

[tex]\textsf{b)} \quad a=24t-6[/tex]

c)   1.5 s

d)  -19.25 m

e)   24.5 m

Step-by-step explanation:

Displacement

[tex]x=4t^3-3t^2-18t+1[/tex]

(where t ≥ 0 and x is in meters)

To find the equation for velocity, differentiate the equation for displacement:

[tex]\implies v=\dfrac{\text{d}x}{\text{d}t}=12t^2-6t-18[/tex]

(where t ≥ 0 and v is in meters per second)

To find the equation for acceleration, differentiate the equation for velocity:

[tex]\implies a=\dfrac{\text{d}v}{\text{d}t}=24t-6[/tex]

(where t ≥ 0 and a is in meters per second squared)

The particle comes to rest when its velocity is zero:

[tex]\begin{aligned}v & = 0\\\implies 12t^2-6t-18 & = 0\\6(2t^2-t-3) & = 0\\2t^2-t-3 & = 0\\2t^2-3t+2t-3 & = 0\\t(2t-3)+1(2t-3) & = 0\\(t+1)(2t-3) & = 0\\\implies t & =-1, \dfrac{3}{2}\end{aligned}[/tex]

As t ≥ 0, the particle comes to rest at 1.5 s.

Substitute the found value of t from part (c) into the equation for displacement to find where the particle comes to rest:

[tex]\implies 4(1.5)^3-3(1.5)^2-18(1.5)+1=-19.25\: \sf m[/tex]

We have determined that the particle is at rest at 1.5 s.

Therefore, to find how far the particle traveled in the first 2 seconds, we need to divide the journey into two parts: before and after it was at rest.  

The first leg of the journey is the first 1.5 s and the second leg of the journey is the next 0.5 s.

At the beginning of the journey, t = 0 s.

[tex]\textsf{when }t=0: \quad x=4(0)^3-3(0)^2-18(0)+1=1[/tex]

Therefore, when t = 0, x = 1

When t = 1.5 s, x = -19.25 m (from part (d)).

⇒ Total distance traveled in first 1.5 s = 1 + 19.25 = 20.25 m

When t = 2, x = -15 m.

Therefore, the particle has traveled 19.25 - 15 = 4.25 m in the last 0.5 s of its journey.

Total distance traveled:

1 + 19.25 + 4.25 = 24.5 m

Refer to the attached diagram

When the particle is at rest, it changes direction.  If we model its journey using the x-axis, for the first leg of its journey (0 - 1.5 s) it travels in the negative direction (to the left). At 1.5 s it stops, then changes direction and travels in the positive direction (to the right), arriving at -15 at 2 seconds.

Answer: x = 2

Step-by-Step Solution:

Given:

OH = WO = LW

OH = 2x + 1

WO = 3x - 1

LW = 5

To Find:

The value of 'x'

Solution:

We know, OH = WO = LW

So, equate any two of the values given :-

2x + 1 = 5

2x = 5 - 1

2x = 4

x = 4/2

x = 2

Hence, x = 2.

The dataset 78 is an outlier of the dataset

The dataset is given as:

1, 12, 13, 15, 18, 20, 35, 37, 40, 78

Where

Q1 = 13

Q3 = 37

The boundaries of the outliers are given as:

L = Q1 - 1.5 * (Q3 - Q1)

U = Q3 + 1.5 * (Q3 - Q1)

Substitute the known values in the above equation

L = 13 - 1.5 * (37 - 13) = -23

U = 37 + 1.5 * (37 - 13) = 73

This means that the data elements outside the range -23 to 73 are outliers.

78 is outside this range

Hence, 78 is an outlier of the dataset

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The half-life of the substance is 1.94 years.

The exponential decay formula aids in determining the exponential drop, which is a rapid reduction over time. To calculate population decay, half-life, radioactivity decay, and other phenomena, one uses the exponential decay formula. F(x) = a [tex](1-r)^{x}[/tex] is the general form.

Here

a = the initial amount of substance

1-r is the decay rate

x = time span

The correct form of the equation is given as:

[tex]a=a_{0}[/tex]×[tex](0.7)^{t}[/tex]

where t is an exponent of 0.7 since this is an exponential decay of 1st order reaction

Now to solve for the half life, this is the time t in which the amount left is half of the original amount, therefore that is when:

a = 0.5 a0

Substituting this into the equation:

0.5 [tex]a_{0}=a_{0}[/tex]×[tex](0.7)^{t}[/tex]

0.5 = [tex](0.7)^{t}[/tex]

Taking the log of both sides:

t log 0.7 = log 0.5

t = log 0.5 / log 0.7

t = 1.94 years

The half life of the substance is 1.94 years.

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Considering their graphs, the interval in which both functions are positive is:

(0, 2)

A function is positive when it's graph is positioned above the x-axis.

Looking at the graph, the functions are positive for x between 0 and 2, hence the interval in which both functions are positive is stated as follows:

(0, 2)

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Option A is correct. The type of construction that we have here is the bisection of the <D.

The bisection of angle can be defined to be the construction of a ray that would help to divide a particular angle into two equal halves.

In this diagram we can see that the angle here is at D. Hence the construction is aimed at dividing this particular angle into 2. Therefore the answer to the question is The bisection of ∠D.

The bisector does the job of creating an equal measure. The given bisector is known to have the midpoint of the segment. It cuts through this angle and creates two different angles that are of the same size.

If we draw the line in that shape, we will be having the division of that angle. From the explanation here, we can see the answer is the first option

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Answer:

Nope.  It would take 32 and 4/13 minutes, which is longer than 30 min.

Step-by-step explanation:

The distance is 35 miles and the speed 65 miles/hour

Dividie the distance by the speed to obtian the time required,

(35 miles)/(65 miles/hour) = 0.538 hours

No, 35 miles at the speed limit of 65 mph would require 0.538 hours, 0.038 hours more than 1/2 hour.  2 and 4/13 minutes more than 30 minutes.